You have to pair the Youtube app with your Youtube account on your mobile phone under All Apps. It's very easy, the steps are listed. After pairing, you start the Youtube app and your videos or films (purchased/rented from Google Play Films) are also displayed here. Start the film via the Youtube app and that's it.

Mirroring your mobile phone is also possible, but you have to activate the function in your mobile phone beforehand. However, the transmission quality was not good for me. I find it better to use the YouTube app, the quality is excellent.